各向同性谐振子径向基本算符的应用

利用基本算符D/Dρ,ρ,1/ρ对本征函数RNL的递推关系和任意力学量算符对函数RNL的作用结果,容易求得力学量的矩阵元和平均值等。     

Particle and power balance in fusion plasma with different fuelling scenarios and helium ash removal

The time evolution of plasma density, temperature and thermal alpha-particle density are considered through modelling of helium ash removal. It is shown that a slow variation of the helium ash density with time can be used for operation path changing in deuterium-tritium fusion plasma. Also, the effect of different fuelling rate scenarios on the plasma operation path and steady state parameters is considered. The temporal evolution of the operating point during the ignition access and ignited operation phases are analyzed analytically and numerically. The main target of the study is the optimization of the plasma operation scenario in future fusion reactors including ITER.     

The theoretical research of basic function method in incompressible viscous flow and its simulations in three-dimensional aneurysms

Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two- and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied. Supported by the National Natural Foundation of China (Grant Nos. 40874077, 40504020, and 40536029) and the National Basic Research Program of China (Grant No. 2006CB806304)     

A remark on He’s variational iteration technique for solving nonlinear equations

The variational iteration method (VIM) can be usefully applied for solving many linear and nonlinear scientific and engineering problems. In this note we show that He’s approach for solving nonlinear equations, arising from the VIM, is, actually, Schröder’s method presented in his classical work from 1870.     

一类捕食者存在疾病的捕食系统传染病模型

建立并分析一类捕食者存在疾病的捕食系统传染病模型,模型中不考虑疾病对捕获率的影响.通过极限系统理论、Lyapunov稳定性理论分析和Bendixson判据,给出了各类平衡点存在及其全局稳定的条件,并得到了捕食者绝灭和疾病成为地方病的充分必要条件.     

带有免疫反应的病毒动力学模型的全局稳定性

利用Lyapunov函数研究了带有免疫反应的病毒动力学模型的全局稳定性.当基本再生数R0≤1时.病毒在体内清除;当R0>1时,病毒在体内持续生存.并且模型的正解当免疫再生数R1≤1时,趋于无免疫平衡点,当R1>1.趋于地方病平衡点.     

A Simple Construction of Gabor Frames for L^2（R）

In this paper, we give a method which allows us to construct a class of Parseval frames for L2 (R) from Fourier frame for L2 (I). The result shows that the function which generates a Gabor frame by translations and modulations has "good" properties, i.e., it is sufficiently smooth and compactly supported.     

多种变质性物品的经济批量问题

本文考虑了多种变质性物品在同一台设备上生产的最优基本生产周期问题。本文采用了基本周期法,给出了问题的数学模型,分析了模型最优解的存在性,并给出了求解该模型的算法和算例,从算例的结果说明基本周期法比公共周期法解决经济批量问题更优。     

Lattice quantization error for redundant representations

Redundant systems such as frames are often used to represent a signal for error correction, denoising and general robustness. In the digital domain quantization needs to be performed. Given the redundancy, the distribution of quantization errors can be rather complex. In this paper we study quantization error for a signal X in represented by a frame using a lattice quantizer. We completely characterize the asymptotic distribution of the quantization error as the cell size of the lattice goes to zero. We apply these results to get the necessary and sufficient conditions for the asymptotic form of the White Noise Hypothesis in the case of the pulse-code modulation scheme.     

Epidemic thresholds for infections in uncertain networks

Over the last 10 years, the field of mathematical epidemiology has piqued the interest of complex‐systems researchers, resulting in a tremendous volume of work exploring the effects of population structure on disease propagation. Much of this research focuses on computing epidemic threshold tests, and in practice several different tests are often used interchangeably. We summarize recent literature that attempts to clarify the relationships among different threshold criteria, systematize the incorporation of population structure into a general infection framework, and discuss conditions under which interaction topology and infection characteristics can be decoupled in the computation of the basic reproductive ratio, R₀. We then present methods for making predictions about disease spread when only partial information about the routes of transmission is available. These methods include approximation techniques and bounds obtained via spectral graph theory, and are applied to several data sets. © 2008 Wiley Periodicals, Inc. Complexity, 2009